Answer:
Given :-
- The mean of 10, 12, 18, 13, P and 17 is 15.
To Find :-
Formula Used :-
[tex]\clubsuit[/tex] Mean Formula :
[tex]\small \bigstar \: \: \sf\boxed{\bold{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}}}\: \: \: \bigstar\\[/tex]
Solution :-
Given :
- Mean = 15
- Sum of all observations = 10, 12, 18, 13, P, 17
- Total Number of Observations= 5
According to the question by using the formula we get,
[tex]\small \implies \bf Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}\\[/tex]
[tex]\implies \sf 15 =\: \dfrac{10 + 12 + 18 + 13 + P + 17}{6}\\[/tex]
[tex]\implies \sf 15 =\: \dfrac{22 + 18 + 13 + P + 17}{6}\\[/tex]
[tex]\implies \sf 15 =\: \dfrac{40 + 13 + P + 17}{6}\\[/tex]
[tex]\implies \sf 15 =\: \dfrac{53 + P + 17}{6}\\[/tex]
[tex]\implies \sf 15 =\: \dfrac{53 + 17 + P}{6}\\[/tex]
[tex]\implies \sf 15 =\: \dfrac{70 + P}{6}\\[/tex]
By doing cross multiplication we get,
[tex]\implies \sf 70 + P =\: 15(6)[/tex]
[tex]\implies \sf 70 + P =\: 15 \times 6[/tex]
[tex]\implies \sf 70 + P =\: 90[/tex]
[tex]\implies \sf P =\: 90 - 70[/tex]
[tex]\implies \sf\bold{P =\: 20}\\[/tex]
[tex]\sf\bold{\underline{\therefore\: The\: value\: of\: P\: is\: 20\: .}}\\[/tex]